1,503 research outputs found
A note on vertex-transitive non-Cayley graphs from Cayley graphs generated by involutions
AbstractWe show that the result of Watkins (1990) [19] on constructing vertex-transitive non-Cayley graphs from line graphs yields a simple method that produces infinite families of vertex-transitive non-Cayley graphs from Cayley graphs generated by involutions. We also prove that the graphs arising this way are hamiltonian provided that their valency is at least six
A combinatorial approach to the power of 2 in the number of involutions
We provide a combinatorial approach to the largest power of in the number
of permutations with , for a fixed prime number . With this
approach, we find the largest power of in the number of involutions, in the
signed sum of involutions and in the numbers of even or odd involutions.Comment: 13 page
On the prime graph of simple groups
Let be a finite group, let be the set of prime divisors of
and let be the prime graph of . This graph has vertex set
, and two vertices and are adjacent if and only if contains
an element of order . Many properties of these graphs have been studied in
recent years, with a particular focus on the prime graphs of finite simple
groups. In this note, we determine the pairs , where is simple and
is a proper subgroup of such that .Comment: 11 pages; to appear in Bull. Aust. Math. So
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